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%I #16 Aug 11 2014 22:45:21
%S 28,108,6902,16068,30662,84662,117157,175844,305804,636268,760436,
%T 765402,1343537,1433493,2125253,3125825,3255917,4264947,4796654,
%U 10271188,11911557,12043892,15344303,27692262,28112662,28478708
%N Origin numbers: integers unreachable by Bergerson's Alpha construction (see the Ross Eckler link).
%C Note that Bergerson's Alpha construction is applied to composite numbers only. Otherwise the sequence could not contain numbers which are twice a prime, like 30662 and 84662. - _Giovanni Resta_, Mar 11 2013
%D R. K. Guy, Unsolved Problems in Number Theory, F31. Japanese edition, 1983. [The English edition is different.]
%H Giovanni Resta, <a href="/A068196/b068196.txt">Table of n, a(n) for n = 1..64</a>
%H A. Ross Eckler, <a href="http://digitalcommons.butler.edu/wordways/vol43/iss2/2">Howard Bergerson</a>, Word Ways: 43:2 (2010), Article 2. [<a href="http://www.thefreelibrary.com/Howard+Bergerson-a0226457883">alternate link</a>]
%e The number 87 is not in the sequence because it can be reached from 90 = 2*3*3*5, since 87 = 90-2-3-3+5. - _Giovanni Resta_, Mar 11 2013
%t seq[n_] := Block[{T = 0*Range@n, f, m}, m[{p_,e_}] := p*Range[-e,e,2]; Do[f = FactorInteger@z; If[Last/@f != {1}, T[[Select[z + Union[ Total /@ Tuples[m /@ f]], 0 < # <= n &]]] = 1], {z, 4, 2*n+4}]; Flatten@Position[T,0]]; seq[10^5] (* _Giovanni Resta_, Mar 11 2013 *)
%K nonn
%O 1,1
%A _Naohiro Nomoto_, Mar 23 2002
%E Edited with three more terms based on the Ross Eckler article by _Omar E. Pol_, Sep 11 2010
%E a(10)-a(26) from _Donovan Johnson_, Oct 05 2010